Modelling of Instabilities in Magnetoelastic Membranes
Thin materials may exhibit instabilities when placed under large loads. In addition to the commonly known buckling phenomena that occur under compressive loading, thin tubular membranes also demonstrate a further limit point elastic instability leading to sudden large deformations when placed under hydrostatic load. Magnetoelastic membranes, which may have application in structural and aerospace engineering, are subject to further limit point instabilities related to an applied magnetic load. The unstable behaviour of these magnetic field-responsive tubular membranes is examined using computational methods.
Tasks & Achievements:
✅ Developed a novel multi-physics numerical model for coupled magneto-elastic problems, addressing complex interactions between magnetic and elastic fields.
✅ Implemented a robust non-linear solution scheme to ensure accuracy under unstable conditions, enhancing model reliability.
✅ Analyzed unstable limit point behavior in thin toroidal membranes, contributing to the understanding of structural instabilities.
✅ Integrated a hp-adaptive mesh refinement scheme using the open-source C++ FEM library deal.II, optimizing computational efficiency and accuracy.
This work is conducted using the open-source, high-performance deal.II finite element library.